Abstract.
This paper introduces an exact primal augmentation algorithm for solving general linear integer programs. The algorithm iteratively substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine inequalities. We prove that various versions of our algorithm are finite. It is a major concern in this paper to show how the subproblem of replacing a column can be accomplished effectively. An implementation of the presented algorithms is given. Computational results for a number of hard 0/1 integer programs from the MIPLIB demonstrate the practical power of the method.
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Received: April 23, 2001 / Accepted: May 2002 Published online: March 21, 2003
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ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
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ID="#"Supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET program TMR ERB FMRX-CT98-0202.
Mathematics Subject Classification (1991): 90C10
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Haus, UU., Köppe, M. & Weismantel, R. A primal all-integer algorithm based on irreducible solutions. Math. Program., Ser. B 96, 205–246 (2003). https://doi.org/10.1007/s10107-003-0384-8
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DOI: https://doi.org/10.1007/s10107-003-0384-8